This invention relates generally to signal processing systems, and more particularly, to systems for estimating the true or underlying value of a time-varying signal, based upon prior observed values assumed by the signal and on the statistics of noise components affecting the value of the observations.
In many applications, such as in communications, an observed electrical signal may contain components derived from external sources of noise, and may also contain components due to variations in the source of the signal itself. In such situations, it is often desired to extract a true or underlying signal from the observed signal. By way of simple example, the underlying signal may be a pure sine wave, and it may be distorted by "phase jitter" in the signal source, causing variations in the phase of the signal, and by noise components introduced between the source of the signal and the Point at which it is observed. This is a problem commonly encountered in communications systems, and a well known technique for determining the phase of such a signal utilizes a phase-locked loop. It will be appreciated, however, that techniques of a more general nature for determining the value of an underlying signal from observed values of the signal would have application in areas other than those of phase-locked loops. Such applications are not limited to electrical or communications systems, but encompass any situation in which a time-varying quantity can be represented as an analog or digital electrical signal, which can then be processed to obtain an estimate of the true or underlying value of the related time-varying quantity.
For purposes of further illustration, it can be assumed that the source of such a time-varying quantity, or its electrical signal counterpart, is capable of assuming any of a finite number of states, or may be closely represented by a finite number of states. In general, it is possible to derive a set of probabilities defining the likelihood that the source state will change from one state to another, either by making use of a priori information or from the observations. These probabilities will define some types of state-to-state moves as relatively easy, i.e. having a high probability, others as relatively difficult, i.e. having a low probability, and some as impossible, i.e. having a zero probability. For example, if the underlying time varying quantity is a sine wave signal the signal will move from state to state in such manner to define the sine function. For this perfect case, the source state will have a one-hundred percent probability of moving to the next state defining the sine function and a zero probability of moving to all other states. If, however, the source is imperfect in some respect, there may be, for example, only a ninety-percent probability of moving to the proper state defining the sine function, a five-percent probability of moving too far, i.e., beyond the state corresponding with the perfect sine function, and a five-percent probability of not moving far enough. In this example, then, the underlying signal is still a sine wave, but the observed signal may depart from the ideal to a degree defined, in part, by the probabilities of the various state-to-state moves. In practice the underlying source is further masked by noise components or other sources of signal uncertainty affecting the observed signal.
The foregoing relatively simple example of probabilities of state-to-state moves is indicative of phase uncertainty, or phase jitter, of a sine wave source. Other parameters of the sine wave, such as peak amplitude and frequency, are assumed to be constant, and the source may be said to be defined by a one-dimensional state space. By way of contrast, a multi-dimensional state space defines the state-to-state probabilities when simultaneous variations in more than one parameter, such as phase and frequency, are possible.
As will be further explained below, it is a principal object of this invention to provide a signal processing module of general application, capable of generating an estimate of the current state of an underlying source based on the observed current state and previous states of an observed quantity related to the source and referred to as the signal, taking into consideration the effects of noise. To this extent, the invention is related to a Markov process, which may be defined as a process in which the probability distribution of the present state of a quantity is completely determined by the most recent prior state of that quantity.
Since, in a narrow sense, the invention can operate in the manner of a phase-locked loop, phase-locked loops can be viewed as the closest prior art to the present invention. However, phase-lock loops cannot be applied in the solution of more complex problems in which the signal source is to be analyzed in terms of its state values in a multi-dimensional state space, rather than a one-dimensional state space. The present invention is directed to a signal analysis module of the general type described, capable of being combined with other signal processing modules of the same type in order to perform analysis on such complex signal sources.